Democratic countries are sometimes perceived as weak, because the leader of the nation has limited powers.
It was important for USA to show USSR that Kennedy has a full public support and can (and will) do whatever is necessary given the circumstances.
In order to do this press was convincing people that Cuba is an immediate threat to United States, and that people should wholly support their leader. This way Khrushchev knew that Kennedy wont back down due to public opinion.
